What is the answer to log_{4}(x)+4log_{x}(4)=5 ?

The answer to log_{4}(x)+4log_{x}(4)=5 is x=256,x=4

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log_{4}(x)+4log_{x}(4)=5

lo g_{4} (x) + 4 lo g_{x} (4) = 5

x = 256, x = 4

Solution steps

lo g_{4} (x) + 4 lo g_{x} (4) = 5

Apply log rules

lo g_{4} (x) + \frac{4}{lo g _{4} ( x )} = 5

Rewrite the equation with

lo g_{4} (x) = u

u + \frac{4}{u} = 5

Solve

u + \frac{4}{u} = 5 : u = 4, u = 1

u = 4, u = 1

Substitute back

u = lo g_{4} (x),

solve for

x

Solve

lo g_{4} (x) = 4 : x = 256

Solve

lo g_{4} (x) = 1 : x = 4

x = 256, x = 4

Verify Solutions:

x = 256

True

, x = 4

True

The solutions are

x = 256, x = 4

lo g_{4} (x^{2} + 5 x - 8) = 2

lo g_{x} (24) = 5

0.56 = ln (y)

lo g_{0.5} (y) = 5

ln (x - 2) + ln (2 x + 1) = 5

What is the answer to log_{4}(x)+4log_{x}(4)=5 ?
The answer to log_{4}(x)+4log_{x}(4)=5 is x=256,x=4
Solve for x: log_{4}(x)+4log_{x}(4)=5
The solution is x=256,x=4